Magnetic order and spin dynamics in the extended kagome system CaBaCo$_{2}$Fe$_{2}$O$_{7}$

Reim, Johannes

Dissertation / PhD Thesis/Book

FZJ-2015-03285

Magnetic order and spin dynamics in the extended kagome system CaBaCo$_{2}$Fe$_{2}$O$_{7}$

Reim, J. (Corresponding Author)FZJ*

2015
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich
ISBN: 978-3-95806-097-5

Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich. Reihe Schlüsseltechnologien / Key Technologies 115, VIII, 144 S. (2015) = RWTH Aachen, Diss., 2015

Please use a persistent id in citations: http://hdl.handle.net/2128/9426

Abstract: The extended kagome system in the hexagonal Swedenborgite structure displays similarly to the pyrochlores a highly frustrated network of tetrahedrally coordinated magnetic ions. These ions form stacked kagome and triangular layers resulting in double tetrahedra columns perpendicular to said layers. However, its broken inversion symmetry raises further the complexity of ordering due to non-vanishing Dzyaloshinskii-Moriya interactions. Recently investigated compounds of this family show various signs for unusual geometric frustration and disordered ground states despite of the typically strong antiferromagnetic exchange. In the present thesis, the magnetic order and the spin dynamics observed on the antiferromagnetically coupled material CaBaCo$_{2}$Fe$_{2}$O$_{7}$ a Swedenborgite are studied in detail. As a primary tool for the experimental investigation, different types of neutron scattering instruments have been used. The experiments are complemented from the theoretical side with Monte Carlo simulations for the modelling of the magnetic order and spin dynamics simulations for the determination of the excitations. Both methods are based on the same Heisenberg nearest neighbour model, in which the in-plane J$_{in}$ and out-of-plane J$_{out}$ exchange interactions are distinguished. In the phase diagram determined using this model an antiferromagnetically ordered phase was found for ratios $\tau$ = J$_{out}/J_{in} \geq$ 1.5 and a 3D spin liquid at lower ratios. The double tetrahedron formed by a triangle of the kagome and two sites of different triangular lattices was found to be the essential building block for the magnetic structure. From the so-called sum rule for the building block derived from the energy minimization follows, that the triangular spins align parallel and the sum of the kagome spins compensates the triangular spins weighted with ratio $\tau$. Thus, in the spin liquid phase the kagome spins tilt with regard to the antiferromagnetically ordered spin structure depending on the ratio of the interactions. In most materials of this compound family, the deviation is so high that only short range order is present. So far, CaBaCo$_{2}$Fe$_{2}$O$_{7}$ is the only known compound of this family, which exhibits a long-range three dimensional order, without a structural transition to an orthorhombic symmetry. This alone already makes the present material unique and interesting as a model system for understanding the interactions and the influence of geometric frustration. A commensurate magnetic order with a $\sqrt{3}$ x $\sqrt{3}$ larger unit cell was reported to arise below 160 K. Using high-resolution powder as well as single crystal diffractometers, a long-periodic modulation was observed in addition to the commensurate magnetic order. The long periodic modulation is only present within the kagome and triangular layers, with the order remaining commensurate perpendicular to the layers. The period of the modulation found to be temperature-independent corresponds to a periodicity of about 370Å or 58 crystallographic unit cells and a propagation vector $\textbf{k} \approx$ (0.342, 0.342, 0). The scattering pattern observed in neutron single crystal measurements is related to a multi-$\textit{q}$ antiferromagnetic structure with $\textbf{k}$ and its symmetrically equivalents. In order to investigate the spin structure related to the long periodic order, neutron scattering experiments with polarization analysis were performed. From the polarization channels, the scattering contributions from moments parallel and perpendicular to the scattering plane as well as the chiral magnetic scattering, a scattering contribution sensitive to vectorial chirality, have been separated. These reveal that the long periodic spin structure (prominent in intensity below 20 K) is canted more strongly in comparison to the more coplanar spin structure in the case of the commensurate order (prominent in intensity above 80 K). A continuous reorientation between the two spin structures is visible in neutron scattering as well as magnetisation data. With the broken inversion symmetry the Dzyaloshinskii-Moriya (DM) interactions can be present. A suitable choice of DM vectors was shown to create energy minima in the energy-vs-reciprocal [...]

Note: RWTH Aachen, Diss., 2015

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